Sensitivity analysis for unmeasured confounding in a marginal structural Cox proportional hazards model

Sensitivity analysis for unmeasured confounding should be reported more often, especially in observational studies. In the standard Cox proportional hazards model, this requires substantial assumptions and can be computationally difficult. The marginal structural Cox proportional hazards model (Cox proportional hazards MSM) with inverse probability weighting has several advantages compared to the standard Cox model, including situations with only one assessment of exposure (point exposure) and time-independent confounders. We describe how simple computations provide sensitivity for unmeasured confounding in a Cox proportional hazards MSM with point exposure. This is achieved by translating the general framework for sensitivity analysis for MSMs by Robins and colleagues to survival time data. Instead of bias-corrected observations, we correct the hazard rate to adjust for a specified amount of unmeasured confounding. As an additional bonus, the Cox proportional hazards MSM is robust against bias from differential loss to follow-up. As an illustration, the Cox proportional hazards MSM was applied in a reanalysis of the association between smoking and depression in a population-based cohort of Norwegian adults. The association was moderately sensitive for unmeasured confounding.